Related papers: Matrix Theory on Noncommutative Torus

We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the…

A unitary matrix model is proposed as the large-N matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary D-particles on the compact space, and admits membrane states with nonzero…

One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically,…

This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with…

We study the Matrix theory description of M-theory compactified on $T^4$ and $T^5$. M-theory on $T^4$ is described by the six dimensional (2,0) fixed point field theory compactified on a five torus, $\widetilde T^5$. For M-theory on $T^5$…

It is known that if we compactify D0-branes on a torus with constant B-field, the resulting theory becomes SYM theory on a noncommutative dual torus. We discuss the extension to the case of a H-field background. In the case of constant…

We describe free differential algebras for non-abelian one and two form gauge potentials in four dimensions deriving the integrability conditions for the corresponding curvatures. We show that a realization of these algebras occurs in…

We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…

We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild geometric assumptions, an orientation-preserving leafwise…

We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding…

We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of…

In this paper we study the compactification conditions of the M theory on D-dimensional noncommutative tori. The main tool used for this analysis is the algebra A(Z^D) of the projective representations of the abelian group Z^D. We exhibit…

In this thesis we will discuss various aspects of noncommutative geometry and compactified Little-String theories. First we will give an introduction to the use of noncommutative geometry in string theory. Thereafter we will present a proof…

The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E_d(Z) U-duality invariant mass formula incorporating…

Noncommutative geometry is based on an idea that an associative algebra can be regarded as "an algebra of functions on a noncommutative space". The major contribution to noncommutative geometry was made by A. Connes, who, in particular,…

We present a novel finite-matrix formulation of gauge theories on a non-commutative torus. Unlike the previous formulation based on a map from a square matrix to a field on a discretized torus with periodic boundary conditions, our…

A new transparent proof of the well known good compactification theorem for the complex torus $(\Bbb C^*)^n$ is presented. This theorem provides a powerful tool in enumerative geometry for subvarieties in the complex torus. The paper also…

An anti-torus is a subgroup $<a,b>$ in the fundamental group of a compact non-positively curved space $X$, acting in a specific way on the universal covering space $\tilde{X}$ such that $a$ and $b$ do not have any commuting non-trivial…

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…

In the M(atrix) theory by making the expansions of the matrices around the membrane and four-brane solutions we derive the three- and five-dimensional gauge theories on the dual tori. The explicit forms of solutions yield the dual…